Differentiator (Inverting)

Produce an output proportional to the rate of change of the input over a controlled frequency range.

V1 is a ±1 V, 1 kHz sine wave. The 10 nF input capacitor and RF = 10 kΩ set the differentiation constant. R1 = 1 kΩ limits high-frequency input current, and the 100 pF feedback capacitor reduces high-frequency gain.

$$V_{\mathrm{out}}\approx-R_F C_{\mathrm{in}}\frac{dV_{\mathrm{in}}}{dt}$$ $$V_{\mathrm{out,pk}}\approx2\pi f R_F C_{\mathrm{in}} V_{\mathrm{in,pk}}\approx0.628\,\mathrm{V}$$

The output is most negative when the input rises fastest and near zero at the input crests. The saved view omits the startup transient. The added resistor and feedback capacitor make this a band-limited differentiator rather than a circuit with unbounded noise gain.

Read the results. The saved transient chart uses separate voltage and current panels; the table provides numerical samples. The first voltage probe is green and the second red. The first current probe is blue; a second current probe is purple.

Model limits. The three-terminal op-amp model has implicit ±12 V output limits, 200,000 low-frequency gain and 10 MHz gain-bandwidth product. Supply pins are intentionally absent in this functional model. In Schmitt-trigger and relaxation/integrator oscillator examples, the switching amplifier uses a 100 kHz gain-bandwidth setting to resolve transitions cleanly at the saved time step. It omits detailed slew-rate, input common-mode, output-current and thermal limits.

Try it. Set V1 frequency to 500 Hz; the differentiated output amplitude approximately halves. Restore the original values after comparing the results.